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Abelian actions on compact nonorientable Riemann surfaces
Published online by Cambridge University Press: 02 December 2021
Abstract
Given an integer $g>2$ , we state necessary and sufficient conditions for a finite Abelian group to act as a group of automorphisms of some compact nonorientable Riemann surface of genus g. This result provides a new method to obtain the symmetric cross-cap number of Abelian groups. We also compute the least symmetric cross-cap number of Abelian groups of a given order and solve the maximum order problem for Abelian groups acting on nonorientable Riemann surfaces.
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- Research Article
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- © The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust
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